Acoustic radiation forces generated by ultrasonic standing waves (USW) have useful applications in microfluidics. For example, acoustic radiation force can drive suspended particles toward and concentrate them to a specific position. It is a useful application that can be used in separation, washing or classification of particles and biological cells. Also, USW can increase the antibody-antigen encounter rate.
The radiation force on a spherical object, F, can be derived from the potential function, U, as shown in formula (1) below:
                              F          =                                    -                              ∇                                                                  ⁢                U                                      =                          -                              ∇                                  (                                      V                    ⁡                                          (                                                                                                    f                            1                                                    ⁢                                                      E                            pot                                                                          -                                                                              3                            2                                                    ⁢                                                      f                            2                                                    ⁢                                                      E                            kin                                                                                              )                                                        )                                                                    ,                            (        1        )            
where V is the volume of a sphere with radius r. The parameters f1 and f2 are dimensionless correction factors which consider the compressibility of the object. Epot and Ekin are the time-averaged potential and kinetic energy densities, given by formulas (2)-(5) below:
                                          f            1                    =                      1            -                                                            ρ                  0                                ⁢                                  c                  0                  2                                                            ρ                ⁢                                                                  ⁢                                  c                  2                                                                    ,                            (        2        )                                                      f            2                    =                                    2              ⁢                              (                                  ρ                  -                                      ρ                    0                                                  )                                                                    2                ⁢                ρ                            +                              ρ                0                                                    ,                            (        3        )                                                      E            pot                    =                                    〈                              ρ                2                            〉                                      2              ⁢                              ρ                0                            ⁢                              c                0                2                                                    ,                            (        4        )                                          E          kin                =                                            ρ              0                        ⁢                          〈                              v                2                            〉                                2                                    (        5        )            
where ρ and c are the density and the sound velocity of the sphere. ρ0 and c0 are the density and the sound velocity of the medium. p2 and v2 are the mean-square fluctuation of the incident pressure and velocity of the acoustic field at the particle's location. If the particle is rigid, f1=f2=1. Formula (1) is valid under the conditions that the radius of the sphere is much smaller than the acoustic wavelength λ, of the medium and is much larger than the medium volume element displacement amplitude. If considering only one-dimensional force and a harmonic sound source, the acoustic radiation force can be obtained from formula (6) below:
                    F        =                                            -                              ∂                                  ∂                  z                                                      ⁢                          U              ⁡                              (                z                )                                              =                                    π                              2                ⁢                                  ρ                  0                                ⁢                                  c                  0                  3                                                      ⁢                          (                                                f                  1                                +                                                      3                    2                                    ⁢                                      f                    2                                                              )                        ⁢                          Vp              0              2                        ⁢            v            ⁢                                                  ⁢                                          sin                ⁡                                  (                                      2                    ⁢                    π                    ⁢                                          z                                              λ                        ⁢                                                  /                                                ⁢                        2                                                                              )                                            .                                                          (        6        )            
The force is proportional to the particle volume and the sound wave intensity and is related to the wavelength of the acoustic wave.
On the other hand, quartz crystal microbalance (QCM) based bio-sensing technology has been applied successfully to investigate molecular interactions over the past few years. This technique is useful for detecting both gases and liquids and has proven to be a versatile label-free method. The deficiency of QCM is while operating in a liquid medium, the sensitivity of QCM will be affected by the viscosity and density of the contacting liquid. These effects reduce sensitivity due to liquid damping.
In order to expand the applications of biochips based on QCM, integrating QCM and biochip for enhanced QSW-based biochip detection sensitivity and reduced detection time is necessary.